Asymptotic axial symmetry of solutions of parabolic equations in bounded radial domains

作者：Saldana Alberto^*; Weth Tobias

来源：Journal of Evolution Equations, 2012, 12(3): 697-712.

DOI：10.1007/s00028-012-0150-6

• Rotating plane method
• Foliated Schwarz symmetry
• Asymptotic symmetry
• Omega limit set

We consider solutions of some nonlinear parabolic boundary value problems in radial bounded domains whose initial profile satisfies a reflection inequality with respect to a hyperplane containing the origin. We show that, under rather general assumptions, these solutions are asymptotically (in time) foliated Schwarz symmetric, that is, all elements in the associated omega limit set are axially symmetric with respect to a common axis passing through the origin and nonincreasing in the polar angle from this axis. In this form, the result is new even for equilibria (i.e., solutions of the corresponding elliptic problem) and time periodic solutions.

• 出版日期2012-9